In conclusion, we have studied theoretically the interacting
SSH4 models at half filling using state-of-the-art DMRG method.
We find that the nearest-neighbor interaction can drive the TI (BI) to CDW phase.
Varying the tunnelings, there exist the topological phase transition between TI and BI.
The critical lines of the topological phase transitions correspond to the Luttinger liquids with integer central charges.
We have calculated
entanglement spectrum, entanglement entropy, energy gaps, and CDW order parameter, to identify the interaction-driven CDW phase transitions and phase diagrams. The phase transition to the CDW phase driven by interaction is shown to be a continuous phase transition. The central charges at the phase boundaries are fixed.
We also have studied the topological properties of the spin-1/2 interacting SSH4 model, and find that the repulsive on-site interaction can enhance the TI and suppress the CDW phase.
But the attractive on-site interaction plays the oppositive role.
We also investigate the edge-model of the TIs. In experiment, the entanglement entropy can be measured using quantum interference
of many-body twins of ultracold atoms in optical lattices [1]}.The CDW phase can be detected by time-of-flight in cold atom experiment.
Our work provides new insights into the
many-body physics in systems with topological properties, and may stimulate the quantum simulation of strong-correlated topological insulators with cold
atoms in optical superlattices.
